Different domain names for subsites?

I have a multisite network with several subsites. Is it possible to have one of the subsites appear, to the user, to exist at a different domain name? We are using subdirectory set-up.

So for example:

site.com/subsite1 will be accessible via newname.com, and transparent to the site visitor. Navigating the site will use pretty permalinks like newname.com/about, but the backend and WP files will still all be hosted in the greater network’s hosting account, i.e. site.com/subsite1

I am not sure if this is a matter of domain name forwarding, masking, redirects, or what.